How to make a warped spacetime grid?
I think what you need is proportional editing. If it is activated, Moving the central vertex down will pull surrounding vertices also, while using the chosen proportional editing falloff setting.

More Complicated ideas:


In the offchance that you actually want to generate a mathematically precise surface, you should look at the Extra Objects addon and Add a Mesh-> Math function. 
There are also many many other alternative Solutions that might be useful for different applications, such as the Displacement modifier or maybe even a Force field acting on a soft body by physics animation....